Why Investigate Root Architecture and Water Uptake?

• Spatially variable models are needed as precision agriculture takes hold. (Green et al., 2006)
• 3D models coupling soil waterflow and root uptake could be used to test hypotheses of root permeability, architecture adapatiation, and genotypic affects on uptake and solute transport. (Dorlodot et al., 2007)
• 3D models may help develop better 1D models.

Theory & History

• Root-Soil Water Movement and Solue Model (R-SWMS)
  • Coupling of two models: one focused on whole root system continuinty (Somma et al., 1998) and one focused on (Doussan et al., 1998)
• Richard’s Equation
• One-Dimensional vs Two-Dimensional vs Three-Dimensional
  • Processing power: How many parameters is too many?
• 3D models can tackle some major issues:
  • Different roots have different funcitons.
  • Soil water content is heterogeneous.
  • Water uptake is a passive process

Root-Soil Water Movement and Solute Model (R-SWMS)

• The root-soil water movement and solute model is used to describe the flow of water and nutrients based on gradients towards the root collar.

Richard’s Equation

• The equation is used to describe water flow under unsaturated conditions. It relates water flow based on the gradients caused by matric and gravitational potential, and we add “sink terms” when incorporating root water uptake.

• \(\frac{\partial \theta}{\partial t} = \nabla \cdot [\textbf{K} \nabla(h-z)] - S\)
  
  
  • \(\theta =\) volumetric water content
  • \(t =\) time
  • \(\textbf{K} =\) hydraulic conductivity tensor
  • \(h =\) water pontential on a weight basis
  • \(S =\) sink term representing root water uptake
  • \(z =\) vertical coordinate

Solving Richard’s Equation

• They discretize the root system as a network of connected root nodes.
  
  
• Radial Flow (Soil-Root):
  • \(J_{r} = K_{r}^{*}s_{r}[h_{s}(z)-h_{x}(z)]\)
• Axial Flow (Xylem):
  • \(J_{x} = -K_{x}(\frac{\Delta h_{x}}{l} + \frac{\Delta z}{l})\)
    
    
    • \(K_{r}^{*} =\) intrinsic radial conductivity
    • \(K_{x} =\) xylem conductivity
    • \(h_{s} =\) water potential at the root surface
    • \(h_{x} =\) water potential in the xylem
    • \(s_{r} =\) outer surface of the root segment
    • \(l =\) length of the root segment
    • \(z =\) vertical coordinate
      
      
• These are only valid under normal conditions: no extreme water stress.

Solving Richard’s Equation Cont.

• Iteratively solve the soil and root network flow equations for water flow.
• Since water flow and root network flow are linked by the radial flux equation, they solve \(J_{r}\) for each root segment in a voxel, and sum them to find the sink term for that voxel.

• They can then use this voxel sink term to solve for water flow by voxel.

• \(S_{j} = \frac{\sum\limits_{i}^{n_{i}}{J_{r,i}}}{V_{j}}\)
  
  
  • \(J_{r,i} =\) Radial flow for root segment i
  • \(V_{j} =\) voxel volume: going to be \(1 \ cm^3\)
  • \(n_{i} =\) number of root segments within voxel j
    
    
    
• Model is first solved based on initial soil water potential (\(h_{s}\))
  • Obtained from distance-weighted average of soil water potential at the corners of the soil voxels including root segments.

The Assumptions

• What are the assumptions?
  
  

1. Soil water is preferably taken up at spatial locations where the energy to bring water to the root collar is minimized.
2. Osmotic potential is negligible and root water capacity can be neglected.
   1. Valid under normal conditions. What about water stress?

The Questions

1. How do collar boundary conditions affect uptake?
   
   
2. How does soil texture affect uptake?
   
   
3. Which model parameters have what affect?
   
   
4. Effective sinusoidal day-night cycle?

Methodology: Scenarios

• Colar Boundary Conditions (CBCs)

Methodology: Parameters

• Input reference and varied paramters

Effects of Soil Type

Reference Parameterization with Collar Boundary Condition 1

Effect of the Parameterization on the Root Collar Flux

Effect of Parameterization on the Three-Dimensional Distribution of Water Content

Effect of Parameterization on the Sink-Term Profiles

Effect of Parameterization on the Vertical Distribution of Water Content and Flow Velocity Field

Effect of Parameterization on the Vertical Distribution of Water Content and Flow Velocity Field Cont.

Effect of Parameterization on the Vertical Distribution of Water Content and Flow Velocity Field Cont. 2

Effect of Soil Type

Effect of Soil Type Cont.

Effect of Soil Type Cont. 2

Day-Night Scenario

Effective Sink Term as a Function of Bulk Water Potential and Averaged Water Content

Effective Sink Term as a Function of Bulk Water Potential and Averaged Water Content Cont.

Conclusions

• Well finally…

LaTex Equations

1. \(y = \beta_1 + \beta_2 x + \varepsilon_1\)
2. \(\mu = \displaystyle \frac{\sum\limits_{i=0}^n{x_i}}{n}\)
3. Miscellanious stuff
   1. \(\sqrt{x} \quad \displaystyle \binom{k}{n} \quad \frac{\partial f}{\partial x}\)
   2. \(A \cup B \qquad A \cap B \qquad A \in B\)
   3. \(\Delta \verb/ or / \delta ?\)
   4. \(\displaystyle \int_0^{\infty} f(x) \quad \displaystyle \lim_{x\to\infty}\)
      
      
      1. Wow. Look at all that LaTex

References